*----* MuPAD 2.0.0 -- The Open Computer Algebra System /| /| *----* | Copyright (c) 1997 - 2000 by SciFace Software | *--|-* All rights reserved. |/ |/ *----* Licensed to: Nicolas M. Thiery >> read("testDegreeBounds.mu"): compTGroupF(8,12,0):quit proc InvariantRingTransitiveGroup(n, i, p) ... end Info: Computation of the invariant ring of the 12th transitive permutation\ group on 8 variables in characteristic 0. Info: Module GLIP version 0.4 ready. Type GLIP::doc(); for usage informati\ on. Info: ====================================================================\ ========== Info: Computation of a minimal generating set using SAGBI+linear algebra. Info: Version: $Id: comphead.mu,v 1.2 2001/03/21 17:51:40 nthiery Exp $ Date: Sat May 5 17:33:03 CEST 2001 Host: giulia4.medicis.polytechnique.fr Info: ====================================================================\ ========== Info: degreeBound: from the dimension of the space: 28 Info: secondaryInvariantsSeries: Computation from cycle types Info: secondaryInvariantsSeries: working on cycletype, [0, 4, 0, 0, 0, 0, \ 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [2, 0, 2, 0, 0, 0, \ 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [8, 0, 0, 0, 0, 0, \ 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 0, 0, 2, 0, 0, \ 0, 0] Info: secondaryInvariantsSeries: working on cycletype, [0, 1, 0, 0, 0, 1, \ 0, 0] Info: degreeBound: enhancement from the degrees of the primary invariants:\ 26 Info: degreeBound: enhancement from the size of the group: 18 Info: Constructing a minimal generating set at degree 0 Info: No generators at degree 0 Info: Constructing a minimal generating set at degree 1 Info: Constructing the initial poset at degree 1 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 1 initial monomials . Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 1 Skiped: 0 Char Col: 0 Mgs: 1 Info: 1 20 2862433 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 1: Date: Sat May 5 17:33:06 CEST 2001 Info: Time: 40 ms Info: Memory: 2862 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 1 Info: -------------------------------------- Info: [1, 0, 0, 0, 0, 0, 0, 0] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 2 Info: Constructing the initial poset at degree 1 Info: Constructing the initial poset at degree 2 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 3 initial monomials ... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 3 Skiped: 1 Char Col: 0 Mgs: 2 Info: 2 10 2862433 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 2: Date: Sat May 5 17:33:06 CEST 2001 Info: Time: 10 ms Info: Memory: 2862 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 2 Info: -------------------------------------- Info: [1, 0, 0, 0, 1, 0, 0, 0] Info: [1, 1, 0, 0, 0, 0, 0, 0] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 3 Info: Constructing the initial poset at degree 3 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 7 initial monomials ....... Info: Applying Gauss Elimination Info: Extracting initial monomials that are not hit Info: Dim: 7 Skiped: 3 Char Col: 0 Mgs: 4 Info: 3 10 2862433 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 3: Date: Sat May 5 17:33:06 CEST 2001 Info: Time: 10 ms Info: Memory: 2862 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 4 Info: -------------------------------------- Info: [1, 1, 0, 0, 1, 0, 0, 0] Info: [1, 1, 0, 1, 0, 0, 0, 0] Info: [1, 1, 1, 0, 0, 0, 0, 0] Info: [2, 0, 1, 0, 0, 0, 0, 0] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 4 Info: Constructing the initial poset at degree 4 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 18 initial monomials ........pp.......... Info: Applying Gauss Elimination [7:2]. Info: Extracting initial monomials that are not hit Info: Dim: 18 Skiped: 8 Char Col: 2 Mgs: 8 Info: 4 40 2895201 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 4: Date: Sat May 5 17:33:06 CEST 2001 Info: Time: 40 ms Info: Memory: 2895 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 8 Info: -------------------------------------- Info: [1, 1, 0, 0, 1, 1, 0, 0] Info: [1, 1, 1, 0, 0, 0, 0, 1] Info: [1, 1, 1, 0, 0, 1, 0, 0] Info: [1, 1, 1, 0, 1, 0, 0, 0] Info: [1, 1, 1, 1, 0, 0, 0, 0] Info: [2, 0, 1, 0, 1, 0, 0, 0] Info: [2, 0, 1, 1, 0, 0, 0, 0] Info: [2, 1, 0, 0, 0, 0, 1, 0] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 5 Info: Constructing the initial poset at degree 5 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 37 initial monomials ......pp.p..p...p.pp..p.p.p....p.pp.p..p.p...p.p....... Info: Applying Gauss Elimination [5:2][6:2][8:2]..[12:2]..[16:2]..[21:2]..[25:2]... Info: Extracting initial monomials that are not hit Info: Dim: 37 Skiped: 8 Char Col: 18 Mgs: 11 Info: 5 160 2927969 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 5: Date: Sat May 5 17:33:06 CEST 2001 Info: Time: 160 ms Info: Memory: 2927 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 11 Info: -------------------------------------- Info: [1, 1, 1, 0, 1, 1, 0, 0] Info: [1, 1, 1, 1, 0, 0, 1, 0] Info: [1, 1, 1, 1, 1, 0, 0, 0] Info: [2, 0, 1, 1, 0, 1, 0, 0] Info: [2, 0, 1, 1, 1, 0, 0, 0] Info: [2, 1, 0, 0, 0, 0, 1, 1] Info: [2, 1, 0, 0, 1, 0, 1, 0] Info: [2, 1, 0, 1, 0, 0, 0, 1] Info: [2, 1, 1, 0, 0, 0, 1, 0] Info: [2, 2, 0, 0, 0, 0, 0, 1] Info: [2, 2, 0, 0, 0, 0, 1, 0] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 6 Info: Constructing the initial poset at degree 6 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 79 initial monomials ...........pp.p...p.p.p..pp.pp.p.p.ppp.ppp.p.p.p..p.p.p..pp.pp..p....pp.p.\ ..p.pp.pp.p..p.p.p....p.p......pp..p..p.pp..p.....p..... Info: Applying Gauss Elimination [10:2][11:2][14:2][15:2][16:2][18:3][19:3][20:3][21:3][22:5][23:3][24:6][25:4][26:3][27:2][28:3][29:5][30:4][32:4][33:2][34:2][35:3][36:2][37:3][38:2][39:4][40:2][43:2][44:3][45:5][46:5][47:3][48:2][49:2][50:4][51:2][52:2][53:2][54:3][55:3][56:2].[61:2]..[65:2][66:3].... Info: Extracting initial monomials that are not hit Info: Dim: 79 Skiped: 16 Char Col: 51 Mgs: 12 Info: 6 440 3042657 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 6: Date: Sat May 5 17:33:08 CEST 2001 Info: Time: 440 ms Info: Memory: 3042 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 12 Info: -------------------------------------- Info: [1, 1, 1, 0, 1, 1, 1, 0] Info: [1, 1, 1, 1, 1, 1, 0, 0] Info: [2, 0, 1, 1, 1, 1, 0, 0] Info: [2, 1, 0, 0, 1, 0, 1, 1] Info: [2, 1, 0, 0, 2, 0, 1, 0] Info: [2, 1, 0, 1, 1, 0, 0, 1] Info: [2, 1, 1, 0, 0, 0, 1, 1] Info: [2, 1, 1, 0, 1, 0, 1, 0] Info: [2, 1, 1, 1, 0, 0, 0, 1] Info: [2, 2, 0, 0, 0, 0, 1, 1] Info: [2, 2, 0, 0, 0, 1, 0, 1] Info: [2, 2, 0, 0, 0, 1, 1, 0] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 7 Info: Constructing the initial poset at degree 7 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 151 initial monomials ......................pp...pp.pp.p.p..p.p....p...pp.ppp.p.p.p...p.p.p.p.p.\ p.p.p.p.pp.ppp.p.p.p.ppp.pp.pp..ppp.pppp.pp..p.p..pp.pp.pp.p..p.p.pppp.pp.\ p.p.pp.pp.pp.p..p.p....p.pp.pp...p.pp..pp......p.pp.p.p.p..p.p.ppp.p.p.p.p\ .ppp..p........p......p......p.p.p....p..p... Info: Applying Gauss Elimination [21:2][24:2][25:2][26:2][27:2][29:2][30:2][34:3].[37:2][38:3][39:2][40:2][41:2][44:2].[46:4][47:3][48:2][49:3][50:3][51:2][52:4][53:6][54:6][55:4].[57:4][58:7][59:3][60:6][62:6][63:5][64:5][65:3][66:7][67:8][68:3][69:4][70:5][71:10][72:7][73:11][74:2][75:3][76:7][77:9][78:8][79:10][80:3][81:8][82:12][83:11][84:7][85:10][86:15][87:7][88:9][89:6].[91:12][92:12][93:6][95:3][96:2][97:8][98:12][99:3][100:10][101:4][102:13][103:10][104:4][105:7][106:9][107:12][108:12][109:11][110:9][111:2][112:13][113:14][114:14][115:13][116:11][117:16][118:15][119:14][120:12][121:14][122:13][123:10][124:12][125:10][126:12][127:12][128:10][129:12][130:3][131:9][132:8][133:7][134:4][135:3].[137:4][139:4][140:5][141:4][143:3][145:4][147:5]Info: Extracting initial monomials that are not hit Info: Dim: 151 Skiped: 32 Char Col: 112 Mgs: 7 Info: 7 1130 3272033 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 7: Date: Sat May 5 17:33:10 CEST 2001 Info: Time: 1 s 130 ms Info: Memory: 3272 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 7 Info: -------------------------------------- Info: [1, 1, 1, 1, 1, 1, 1, 0] Info: [2, 1, 0, 0, 2, 0, 1, 1] Info: [2, 1, 1, 0, 1, 0, 1, 1] Info: [2, 1, 1, 0, 2, 0, 1, 0] Info: [2, 1, 1, 1, 0, 0, 1, 1] Info: [2, 1, 1, 1, 1, 0, 0, 1] Info: [2, 2, 0, 0, 0, 1, 1, 1] Info: -------------------------------------- Info: Constructing a minimal generating set at degree 8 Info: Constructing the initial poset at degree 8 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 281 initial monomials .....................................pp.p..p.....p.p.p..p.p.p.p...pp.pp.pp\ .pp..p.p.p.....ppp.pp.p.pp.p.p.ppp.ppp.pp.pp.p.p..ppp.pp.pp..pp.ppp.p.p.p.\ pp..pp.p.p..p.p.p....pp......pp.pppp.pp.ppp.pp.p.p...p.p.p.pp.pp.pp.p.p.pp\ .pp.pp.p.pp.pp.pp..p.p..p..p.p.p.pp.p.p.p.pppp.ppp.ppp.p.pp.pppppp.p.pp.pp\ p.pp..pppp..pp.p.p.p.pp.pppp.ppp.pppp..p.p.pp..p.p.pppp.p.p.ppp.pp..pppp..\ .p..p.pppp.pp.p.p.p.pp..p.....p.p..pp.ppppp.p.pp..p.p.p.pp.pp.p..pp.pp....\ ..p.p..p.p..pp......p.p.pp.p.p.p.p.pp..p.p..p..p.p.p.p.ppp.p......pp..p.p.\ p.............p...p..p...p. Info: Applying Gauss Elimination [36:2][37:2][39:2][44:2][45:2][46:2][48:2][49:2][50:2][51:2][54:2][55:2][56:2][57:3][59:2][60:2][61:2][66:5][67:3][68:3][69:2][70:2][71:3][72:5][73:3][74:5][75:5][76:4][77:4][79:3][80:3][81:3][83:2][84:3][85:3][86:5][87:5][88:3][89:3][90:4][91:6][92:6][94:2][95:3][96:7][100:5][102:2][103:4][104:4][105:3][106:4][107:5][108:5][109:3][110:5][111:2][112:3][115:3][116:2][117:10][118:10][119:6][120:9][121:3][122:8][123:7][124:4][125:6][126:6][127:9][128:8][129:11][130:7][131:9][132:11][133:5][134:9][135:5][136:8][137:13][138:18][139:12][140:9][141:2][142:8][143:15][144:7][145:15][146:4][147:13][148:15][149:14][150:15][151:25][152:22][153:15][154:26][155:10][156:9][157:12][158:4][159:11][160:5][161:15][162:12][163:18][164:15][165:27][166:26][167:20][168:22][169:8][170:4][171:6][172:17][173:7][174:18][175:23][176:22][177:26][178:14][179:14][180:24][181:26][182:24][183:42][184:29][185:26][186:28][187:30][188:38][189:27][190:36][191:18][192:35][193:38][194:34][195:15][196:33][197:23][198:6][199:31][200:45][201:47][202:31][203:37][204:39][205:2][206:8][207:9][208:10][209:25][210:41][211:56][212:23][213:17][214:42][215:29][216:16][217:3][218:9][219:32][220:2][221:2][222:7][223:5][224:19][225:34][226:35][227:36][228:29][229:16][230:34][231:46][232:45][233:45][234:37][235:45][236:47][237:44][238:34][239:35][240:43][241:45][242:44][243:32][244:42][245:36][246:46][247:58][248:57][249:54][250:53][251:42][252:49][253:54][254:39][255:48][256:44][257:50][258:56][259:53][260:46][261:54][262:50][263:52][264:41][265:34][266:40][267:48][268:46][269:36][270:36][271:7][272:32][273:15][274:46][275:40][276:43][277:24][278:40][279:41][280:39]Info: Extracting initial monomials that are not hit Info: Dim: 281 Skiped: 58 Char Col: 223 Mgs: 0 Info: 8 2710 3829089 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 8: Date: Sat May 5 17:33:17 CEST 2001 Info: Time: 2 s 710 ms Info: Memory: 3829 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 0 Info: Constructing a minimal generating set at degree 9 Info: Constructing the initial poset at degree 9 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 490 initial monomials ........................................................................pp\ ...pp.pp.p.pp.........pp...p..p.p....p......p..ppp.pppp.pp.p.p.p..p.....p.\ p.p.p.p.p.p.p.p.p.p.p.p.p.p.p.p..p.p.p.ppp.ppp.pp.ppp.pp.p.p.p.p.p.ppp.p.p\ p..ppp.ppp.ppp..pp.ppp.ppp.ppp.ppp.pp.pp.pp.p.p.ppp.pp.p.pp..p.p.p.pppp.pp\ .pp.pp.p.....pppp.pp.p.ppp.p..p.p.pp.pp.pp.pp.pp..p.ppp.pppp.pppp.pp.pp.pp\ p.pppp.pppp.p.p.pp.p.pp..p.pp.pp..pppp.ppp.ppp.pp.pp.pp...ppp.p.pp.p.ppp..\ p....pp.pp.pp.p...p.pp.....pp.........ppp.pp.ppp.pppp..pp..p.p.p.p.p.pp.p.\ p.p.ppp.pppp.ppp.p.pp.pppp.ppp.pp.ppp.pppp..ppp.p.p.pp.p.pp.p.pp.pp.ppp.pp\ p..pp.pp..pp..p.p.pp.p.p.ppp.ppp..pp.....p....p.p.pp.pp.pp.p.p.pppp.p.p.pp\ p.p..ppp.p.p.pp.p.pp.p.ppppp.ppppp.pppppp.pp.pppp.ppp.p.pppp.p.p.p.pppppp.\ p.ppp.pppppp.pp..ppppppp..p.p..pp..p.p.pp.pp.p......p.ppp.ppp.pp.p.pp.ppp.\ ppp....p..p.pp..p.ppp.p..ppp...ppp....pp.p.p..pp.ppppp.p.p.p..p..p....p...\ ...p....p.ppp.pp.p.p.pp.pp.p.p.p..p.p......p.....p.p.p.ppp.p.p..p...p..p..\ .p.p.p.....p..pp....ppp.....p.p.........p.p Info: Applying Gauss Elimination [71:2][74:2][75:2][76:2][77:2][86:2][89:3][91:3][92:2][96:2][102:4].[104:3][105:4][106:3][107:3][108:3][109:4][111:3][116:3][117:2][118:6][119:5][120:2][121:4][122:3][123:4][124:4][125:7][126:5][127:5][128:2][129:4][130:7][131:3][132:6][134:4][135:2][136:2][137:7][138:8][139:10][140:4][141:6][142:6][143:4][144:2][145:3][146:5][147:7][148:6][149:5][151:3][152:4][153:3][155:2][156:3][157:3][158:8][159:6][160:3][161:6][162:4][163:4][164:2][165:5][166:8][167:4][168:7][170:2][171:3][172:3][173:9][174:5][175:7][176:4][177:6][182:7][183:4][184:4][185:3][186:2][187:6][188:12][189:12][190:6][191:5][192:10][193:12][194:10][195:8][196:5][197:15][198:9][199:15][200:15][201:11][202:4][203:11][204:18][205:15][206:12][207:18][208:11][209:16][210:13][211:15][212:15][213:18][215:4][216:5][217:5][218:23][219:7][220:6][223:3][224:3][225:14][226:7][227:4][228:9][229:16][230:12][231:11][232:8][233:5][234:15][235:20][236:21][239:3][240:17][241:7][245:5][247:11][248:9][249:15][250:17][251:10][252:14][253:14][254:17][255:18][256:10][257:20][259:10][261:3][262:11][263:6][264:30][265:26][266:21][267:18][268:5][269:17][270:23][271:11][272:17][273:26][274:33][275:28][276:44][277:36][278:37][279:47][280:30][281:39][282:18][283:2][284:13][285:16][286:6][287:15][288:22][289:26][290:22][291:40][292:30][293:51][294:41][295:40][296:27][297:29][298:9][299:10][300:21][301:37][302:12][303:29][304:39][305:33][306:32][307:31][308:22][309:21][310:45][311:57][312:42][313:18][314:46][315:35][316:56][317:53][318:53][319:49][320:24][321:61][322:63][323:53][324:55][325:53][326:25][327:55][328:57][329:9][330:26][331:36][332:20][333:41][334:11][335:51][336:44][337:44][338:69][339:77][340:73][341:54][342:73][343:59][344:30][345:9][346:17][347:71][348:41][349:57][350:28][351:69][352:101][353:74][354:54][355:56][356:95][357:98][358:57][359:56][360:23][361:47][362:26][363:51][364:47][365:47][366:60][367:67][368:73][369:6][370:14][371:14][372:65][373:42][374:81][375:100][376:97][377:92][378:74][379:71][380:128][381:62][382:12][383:80][384:46][385:7][386:18][387:46][388:91][389:112][390:32][391:89][392:109][393:84][394:74][395:92][396:75][397:43][398:68][399:58][400:91][401:133][402:121][403:133][404:61][405:121][406:95][407:118][408:107][409:49][410:90][411:105][412:122][413:100][414:105][415:100][416:85][417:108][418:135][419:122][420:60][421:140][422:5][423:121][424:110][425:111][426:134][427:145][428:132][429:107][430:5][431:5][432:138][433:110][434:151][435:135][436:136][437:132][438:126][439:128][440:5][441:102][442:136][443:94][444:137][445:71][446:139][447:143][448:149][449:149][450:142][451:145][452:134][453:140][454:142][455:146][456:145][457:115][458:123][459:134][460:134][461:138][462:154][463:133][464:150][465:130][466:139][467:144][468:141][469:134][470:149][471:144][472:148][473:153][474:149][475:148][476:140][477:130][478:40][479:144][480:67][481:146][482:139][483:132][484:128][485:136][486:122][487:129][488:142][489:142]Info: Extracting initial monomials that are not hit Info: Dim: 490 Skiped: 116 Char Col: 374 Mgs: 0 Info: 9 5960 4926817 #Stats: degree,time(ms),mem(bytes) Info: Statistics for degree 9: Date: Sat May 5 17:33:31 CEST 2001 Info: Time: 5 s 960 ms Info: Memory: 4926 ko. Info: S-Pairs: 0 (+ 0 normalf->0 + 0 reduction->0 + 0 non-lcm->0) Info: Minimal generators: 0 Info: Constructing a minimal generating set at degree 10 Info: Constructing the initial poset at degree 10 Info: Generating the full matrix of decomposable invariants by iterating t\ hrough all 830 initial monomials ..........................................................................\ ..............................ppp.p..p.p.........p.p.p..p.p.p.p......p....\ .....p......p...pp.pp.pp..........pp...pp..p.pp..pp.pp.p.....p....p.......\ ...ppp.pp.p...p.ppp.ppp.pp.ppp